The ultimate objective of our research is the development of S+LongMem, an advanced software toolkit to assist researchers in applying a class of statistical models (long memory processes) of particular importance for biomedical time series (examples of such series are measurements of heart rate variability, renal blood flow and blood pressure, and vasomotion). The application of these statistical models will facilitate more accurate physiological and medical interpretation of biomedical time series recorded for the purpose of detection, identification and classification of disease. The proposed research will contribute to the health sciences by developing 1) a unified framework for properly classifying and analyzing biomedical time series; 2) a guidance system for the use of these tools (and the underlying statistical methodology) so that researchers can identify informative statistics for their data; 3) a comprehensive mechanism for simulating biomedical time series from a wide variety of fitted or postulated models for use in diagnostic testing; and 4) a software toolkit S+LongMem implementing these objectives. This toolkit will be accompanied by an interactive multimedia casebook documenting case studies in applying statistical methodology to biomedical time series.